LCGM OR GMM
Message/Author
 Judy Black posted on Thursday, May 08, 2014 - 5:07 am
Dear Dr. Muthen,

We recently did an analysis with Mplus, in order to identify distinct trajectories of depression over three time points. We would like to compare results of the Latent Class Growth Modeling (LCGM) with the results of Growth Mixture Modeling (GMM). Yet, we are not very clear about how to perform LCGM and GMM in Mplus. As you can see the syntax below, this is a LCGM analysis, am I right? Then, I would wonder, what should the syntax for GMM be?

Judy

ANALYSIS:Type is mixture;
MODEL:
%OVERALL%
i s q|T1CONTR@0 T2CONTR@3 T3CONTR@9;
s@0;
i@0;
q@0;
%C#1%
[i s q];
%C#2%
[i s q];
 Linda K. Muthen posted on Thursday, May 08, 2014 - 7:00 am
LCGM is not a mixture model. See Examples in Chapter 6 of the user's guide. Do you mean LCGA versus GMM? If so, see examples in Chapter 8 of the user's guide.
 Judy Black posted on Friday, May 09, 2014 - 1:12 am

Yes, I mean LCGA versus GMM. I know that LCGA does not allow within class variability, whereas GMM allowes. But I am not very sure how to write the syntax for LCGA and GMM in Mplus. Chapter 8 of the user's guide says that "When TYPE=MIXTURE without ALGORITHM =INTEGRATION is selected, a LCGA is carried out.". Does this mean, the model with "ALGORITHM =INTEGRATION" is actually a GMM? If without "ALGORITHM =INTEGRATION", then the model is a LCGA model? If this is correct, then the model I showed before is actually a LCGA model, right?
 Linda K. Muthen posted on Friday, May 09, 2014 - 9:04 am
Example 8.4 is a GMM. Example 8.9 is a LCGA. If you add ALGORITHM=INTEGRATION to Example 8.9, it is a GMM.

You can also fix the variances of the growth factors to zero to obtain a LCGA.
 Judy Black posted on Monday, June 02, 2014 - 3:02 am
Hi Linda,

In my data, with the use of LCGA, we actually could obtain a 3-class model. However, with the use of GMM, the 2-class model has the bets model fit, but one class contained 99% of the sample, and the other class only contained 1% of the sample. Therefore, with the use of GMM, actually we can only choose a 1-class model.
I also compared the BIC, AIC of the 1-class GMM and the 3-class LCGA. The 1-class GMM has slightly better goodness of fit than the 3-class LCGA. I am a bit of confused, why the results of LCGA and GMM are so different?

Thanks.
 Linda K. Muthen posted on Monday, June 02, 2014 - 10:41 am
It is known that LCGA will find more classes than GMM because it does not allow within class variability.

You can try freeing the variances across classes in the GMM. The default is for them to be held equal.

If you outcome is continuous and skewed, you can try the new methods for this situation introduced in Version 7.2 See the Version 7.2 Language Addendum on the website with the user's guide.
 Louise van Elst posted on Monday, September 28, 2015 - 8:49 am
I would like to run a GMM where the variances are freed across the classes. I have looked in the 7.2 Language Addendum, but I can not find which input I need for this. Could you help? My outcome is continious, but not skewed.

Thank you.
 Bengt O. Muthen posted on Monday, September 28, 2015 - 1:36 pm
Just mention the variances you want free in each class, like

%c#1%
i;
%c#2%
i;
 Loes Pouwels posted on Friday, October 02, 2015 - 6:16 am
I conducted a multivariate LCGM and could find a model with 4 classes with a good fit. However, when I counduct a GMM (with or without variances freed across the classes), I received the following error message:

WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IN CLASS 1
IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/
RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL
TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE
THAN TWO LATENT VARIABLES. CHECK THE TECH4 OUTPUT FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE POI.

I checked the variances and both slopes and one intercept had negative variance. Does this mean that in this case LCGA will be better than GMM? Can I still use the LCGA or are these results not reliable?
 Bengt O. Muthen posted on Friday, October 02, 2015 - 7:58 am
The negative variances may indicate that perhaps the GMM needs fewer classes. Check with BIC.